4 red balls and 5 green balls are selected from n balls. If the sum of both the selections is greater then ^ n+1 C₄ then the value of n is equal to

Step-by-step solution

The problem requires finding for which n the sum of selecting 4 red balls and 5 green balls from n balls each exceeds C ( n +1, 4). The inequality is C ( n , 4) + C ( n , 5) > C ( n +1, 4). Applying Pascal's identity, C ( n , 4) + C ( n , 5) = C ( n +1, 5), so the inequality becomes C ( n +1, 5) > C ( n +1, 4). Expressing both sides with factorials, (n+1)! 5!(n-4)! > (n+1)! 4!(n-3)! , and simplifying leads to n - 3 > 5 , so n > 8 . Given the options, the correct choice is A . Final answer: A